At the same temperature, but under another pressure P' the gas will have a
different volume V'. Since, according to Boyle's law, PV is constant (P'V'
= P_oV_o), it will still equal P_oV_oT / 273. Therefore P_oV_o / 273 is
also constant. This quantity is called "the gaseous constant," and if we
represent it by the symbol R, we obtain the general formula PV = RT for all
gases, or PV / T = R.
Suppose, for instance, we have a gramme-molecule of a gas at 0deg C. in a
space of 1 litre. It has a pressure of 22.35 atmospheres at 0deg C., or
273deg absolute temperature. Since PV = RT, R = PV / T = 1 x 22.35 / 273 =
.0819. This number .0819 is the numerical value of the constant R for all
gases, volume being measured in litres and pressure in atmospheres.
Substances in solution behave exactly like gases, they follow the same laws
and have the same constants. All the conceptions which have been acquired
by the study of gases are applicable to solutions, and therefore to the
phenomena of life. The osmotic pressure of a solution is the force with
which the molecules of the solute, like gaseous molecules, strive to
diffuse into space, and press on the limits which confine them, the
containing vessel being represented by the surfaces of the solution.
Osmotic pressure is measured in exactly the same way as gaseous pressure.
To measure steam pressure we insert a manometer in the walls of the boiler.
In the same way we may use a manometer to measure osmotic pressure. We
attach the tube to the walls of the porous vessel, allow the solvent to
increase in volume under the pressure of the solute, and measure the rise
of the liquid in the manometer tube.
_Pfeffer's Apparatus._--Pfeffer has designed an apparatus for the
measurement of osmotic pressure. It consists of a vessel of porous
porcelain, the pores of which are filled with a colloidal solution of
ferrocyanide of copper. This forms a semi-permeable membrane which permits
the passage of water into the vessel, but prevents the passage of sugar or
of any {19} colloid. The stopper which hermetically closes the vessel is
pierced for the reception of a mercury manometer. The vessel is filled with
a solution of sugar and plunged in a bath of water. The volume of the
solution in the interior of the vessel can vary, since water passes easily
in either direction through the pores of the vessel. The boundary of the
solvent has become extensible, and its volume can increase or diminish in
accordance with the osmotic pressure of the solute. Under the pressure of
the sugar water is sucked into the vessel like air into a bellows, the
solution passes into the tube of the manometer, and raises the column of
mercury until its pressure balances the osmotic pressure of the sugar
molecules.
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